How Can Operations Research Techniques Determine Project Completion Time?

[janani66]

Please help me to solve this problem. This was a question given in our end semester examination.

The management of a certain garment factory is considering the construction of a new washing plant building. The project consists of 7 major activities. The information pertaining to the project is given below.

Activity [/INDENT]Immediate Predecessor

​

Duration
A ---- 2
B ----- 6
C - 4
D A 3
E C 5
F A 4
G B,D,E 2


i) Draw the network diagram.
ii)Find the critical path.
iii) What is the expected time required to complete the project.
iv) Variances of the time duration for each activity of the project are given below. Find the probability that the project will be completed on or before 10 weeks.

Activity variances
A 0.25
B 0.11
C 0.25
D 0.25
E 0.25
F 0.11
G 0.11


I did the whole question in the paper. But I'm not very sure about the Network diagram. Time of the critical path was 11. and that is the answer for iii.

Then for the third part I got 0.36 as the probability. As I'm new to this forum I don't know how to get the symbols to write my answer here. Please can anybody do this question here? then I can compare with my answer.

 

[Valkarie]

Answer: i) Network diagram: A -2-> B -6-> G | / \| / \4 D-3-> E-5-> G||F -4-> Gii) Critical Path: A -> D -> E -> G -> B -> G = 11 Weeksiii) Expected Time Required to Complete the Project: 11 Weeksiv) Probability that the Project will be Completed on or Before 10 Weeks: 0.36

 

[Mene]

I can provide some guidance and suggestions for solving this problem. However, I am not able to provide the exact answer as it is important to use your own knowledge and understanding to solve this type of problem.

Firstly, let's define what Operations Research (OR) is. OR is a field of study that uses mathematical and analytical methods to help make better decisions in a wide range of areas, including business, engineering, and science. In this case, we are using OR techniques to solve a problem related to project management.

Now, let's break down the problem and discuss the steps needed to solve it.

Step 1: Understand the problem

The problem states that a garment factory is considering building a new washing plant and has 7 major activities involved in the project. The duration of each activity and their predecessors are also given.

Step 2: Draw the Network Diagram

To solve this problem, we need to first draw a network diagram. This diagram will help us visualize the project and identify the critical path. The critical path is the longest path in the network and represents the minimum time required to complete the project.

Step 3: Find the Critical Path

To find the critical path, we need to calculate the duration of each path in the network. The path with the longest duration is the critical path. In this case, the critical path is A-D-E-G with a duration of 11 weeks.

Step 4: Calculate the Expected Time

The expected time is the sum of the duration of each activity in the critical path. In this case, the expected time is 11 weeks.

Step 5: Calculate the Probability

To calculate the probability, we need to use the variance and standard deviation of each activity. The formula to calculate the probability of completing the project within a certain time frame is:

Probability = 1 - (standard deviation / expected time)

In this case, the standard deviation is the square root of the variance. Using the given variances, we can calculate the standard deviation for each activity and then use the formula to calculate the probability. The overall probability of completing the project within 10 weeks is 0.36.

In conclusion, solving this problem involves using OR techniques such as network diagrams, critical path analysis, and probability calculations. It is important to carefully understand the problem and use the correct formulas and methods to arrive at the solution. I hope this helps in your understanding of the problem and provides some guidance for solving